For me if you can lead an somewhat active social life, and undertake cleaning jobs, and go on nights out and plan holidays you have some level of dexrity and nous.
All this "couldn't make beans on toast crap" is bollocks
Nor is the children being in their fathers care a red flag.
There is a lot of reference to Shelia been poor with finances.
That's why June used to bring her food parcels, so any money wasn't spent on recreational drugs. When Sheila was on medication the side effects were instability as regards gait, smudged lipstick as noted by shopkeeper Barry Parker that final day, nurse Caroline Heath noticing how unkempt she looked when not told to look smart, which she could do when prompted to do so.
Planning nights out with friends and accomplishing some quality of life were in collision with each other, her working life also being another disaster area. It may have been that June was beginning to realize after her daughter's second breakdown that she couldn't hold down a regular job and some niche sinecure was being arranged for her at Maldon Growers, with the possibility of her living full time at Bourtree Cottage.
Was this what tipped Jeremy over the edge, with the temptation of the vacant Maida Vale flat beckoning, or simply that Sheila was so far gone that final week that he realized now was the chance to put the dastardly plan he had discussed with Julie in to action?